Activist investors — money managers who seek to shake up a company’s strategy in search of huge paydays — have been growing in size and power in the United States, bending the knees of even the biggest corporate titans.

Now, these investors are taking their fights overseas with bigger and bolder bets.

The latest to step onto the global stage is Daniel S. Loeb, who in his first major European campaign is looking to rattle the Swiss food giant Nestlé.

By taking a $3.5 billion stake, including options — his biggest wager to date — Mr. Loeb’s $17.5 billion hedge fund Third Point is betting that Nestlé can rev up its growth if it listens to Third Point’s proposals, which include selling off Nestlé’s stake in L’Oréal. Investors appeared to applaud Mr. Loeb’s gambit, sending shares of Nestlé up 4.3 percent in trading in Zurich on Monday.

Other European giants have entered activists’ cross hairs. This year, Elliott Management, the $33 billion firm run by Paul E. Singer, took on both the Dutch paint maker Akzo Nobel and BHP Billiton, a British-Australian mining firm.

With swelling coffers — activists now manage $121 billion on behalf of private investors, pension funds and sovereign wealth funds — and a growing number of competitors in the United States, some activists are finding more opportunities abroad than at home.

“The U.S. market has lots of activists in it looking for ideas and has been picked over,” said Greg Taxin, managing director of the activist advisory firm Spotlight Advisors and a founder of Glass, Lewis & Company. “If you’re Paul Singer and managing $33 billion, you have to look into other markets, and you have to be sophisticated.”

The biggest American funds are no strangers to venturing abroad in their activist campaigns. Elliott has been willing to take on Samsung, the biggest conglomerate in Asia, and Bank of East Asia in Hong Kong. It even challenged the government of Argentina in a decade-long legal battle over that nation’s debt default.

Mr. Loeb has urged changes at Sony and other Japanese companies. And Nelson Peltz of Trian Partners pushed for changes at the yogurt-and-Evian producer Danone five years ago.

At a hedge fund conference in Las Vegas in May, managers talked about how Europe had transformed from a region of political uncertainty to one with stability. And with the conclusion of many market-moving events, like Britain’s decision to leave the European Union and France’s presidential election, Europe has become a region with more certainty than the United States, where political turmoil swirls around the Trump White House.

At the same time, many European countries lack the sort of obstacles that American companies can throw at activists, said David Hunker, the head of shareholder activism defense at JPMorgan Chase.

“In general, Europe as a whole is easier from an activist perspective,” he said. “The types of structural protections that you have in the U.S., like poison pills or staggered boards, are either much less common or just not permissible in Europe.”

Indeed, Switzerland’s corporate law could provide some help to Mr. Loeb.

In Switzerland, shareholders elect each member of the board individually, meaning that if Mr. Loeb chose to nominate a new board member and that candidate received a majority of the vote, that candidate would be added to the board without a contest.

“It makes it easier for an activist to get someone on the board,” Mr. Taxin said.

On Monday, a representative for Nestlé said in a statement: “As always, we keep an open dialogue with all of our shareholders, and we remain committed to executing our strategy and creating long-term shareholder value. Beyond that, we have no specific comment.”

Mr. Loeb declined to comment for this article.

The ambitious corporate campaigns abroad speak to the maturation of the hedge fund industry, as well as to the growth of American-style activism. Once seen as a small group of loudmouth know-it-alls and viewed with suspicion by big institutional shareholders like state pension funds, in recent years, activist investors like Mr. Peltz and William A. Ackman have at times been welcomed by these same shareholders and seen as a positive force for change in a recalcitrant company.

These same institutional shareholders have in turn begun to see activism as a lucrative investment, pouring billions into activist hedge funds.

With more money in the sector, and more activists searching for companies to wage campaigns against, the landscape in the United States has become crowded.

When Mr. Loeb disclosed a large position in the auction house Sotheby’s in 2013, he became the third activist at the company, joining Trian Partners and Marcato Capital Management. Hertz, the car-rental company, found itself under siege by two major activist investors. As soon as Mondelez International finally acquiesced to one activist, Trian, by giving it a seat on the board, Mr. Ackman, of Pershing Square Capital Management, showed up.

Finding new targets in Asia or Europe is no guarantee of success. So far, the activists’ record abroad has been mixed.

Despite pressure from Elliott, Akzo Nobel rebuffed a takeover attempt by its American rival PPG Industries. Mr. Loeb’s battle against the Sony Corporation lost steam when he was unable to persuade the company to sell part of its entertainment unit.

Foreign campaigns also come with their own challenges, notably shareholders suspicious of American interlopers.

Eleazer Klein, a partner at Schulte Roth & Zabel who oversees that law firm’s global shareholder activism group, said, “A lot of the share ownership is in the hands of people who don’t think the same way that U.S. institutions think.”

Many companies that are listed in Europe and in Asia have one large shareholder that is either a family or the government, something that is less common in the United States, Mr. Klein said.

Yet mutual fund giants like BlackRock and T. Rowe Price have increasingly become big shareholders in companies around the world. Such firms have often indicated a willingness to back activists to bolster a company’s stock price.

Still, American hedge funds like Elliott and Third Point have learned to be mindful of local culture and tend to conduct less overtly hostile campaigns.

Mr. Loeb has forged a reputation for writing stinging criticisms in so-called poison-pen letters to corporate chieftains. So far, however, Mr. Loeb has had only praise for Nestlé’s chief executive of six months, Ulf Mark Schneider, writing in a letter to investors that Mr. Schneider had “an impressive track record.”

While hedge fund and private equity managers have become an accepted part of the corporate world, in Europe there is still some hostility toward these private investors.

Franz Müntefering, a former head of the Social Democratic Party of Germany, once called American investors “swarms of locusts that fall on companies, stripping them bare before moving on.”

Mr. Hunker, of JPMorgan Chase, said: “We’re still waiting for the European institutional set to be as open to activists as their American counterparts are. With an iconic British or French company, are the big local pension funds willing to vote their shares in favor of an activist?”

Correction:

An earlier version of this article misstated, in the initial reference, the name of a hedge fund led by Nelson Peltz. As correctly mentioned elsewhere in the article, the fund is Trian Partners, not Trian Fund Management.

Correction:

An earlier version of a listing of Nestle’s operations with this article misstated the amount of revenue from pet sales last year. It was $12.4 billion, not $12.4 million.

A version of this article appears in print on , on Page B1 of the New York edition with the headline: With Crowding in U.S. Market, Activist Investors Look to Europe. Order Reprints | Today’s Paper | Subscribe